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NCERT Solutions Class 12 Maths Chapter 7 - Integrals

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1 	 / 	 1 8
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 6
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 8 .
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A n s . 	
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1 	 / 	 1 8
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 6
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 8 .
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1 	 / 	 1 8
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 6
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 8 .
1 . 	 	
A n s . 	
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[ A p p l y i n g 	 p r o d u c t 	 r u l e ]
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2 . 	
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1 	 / 	 1 8
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 6
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 8 .
1 . 	 	
A n s . 	
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2 . 	
A n s . 	
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1 	 / 	 1 8
N C E R T 	 s o l u t i o n
C h a p t e r 	 - 	 7
I n t e g r a l s 	 - 	 E x e r c i s e 	 7 . 6
I n t e g r a t e 	 t h e 	 f u n c t i o n s 	 i n 	 E x e r c i s e s 	 1 	 t o 	 8 .
1 . 	 	
A n s . 	
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[ A p p l y i n g 	 p r o d u c t 	 r u l e ]
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2 . 	
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FAQs on NCERT Solutions Class 12 Maths Chapter 7 - Integrals

1. What are integrals?
Ans. Integrals are mathematical tools used to find the area under a curve or the accumulation of a quantity over a given interval. They are used to solve problems in calculus, such as finding the area of irregular shapes or calculating the total distance traveled by an object.
2. How do you find the integral of a function?
Ans. To find the integral of a function, you can use various methods, such as the power rule, substitution, or integration by parts. The process involves finding an antiderivative of the function, which is another function whose derivative is equal to the original function.
3. What is the significance of integrals in real-life applications?
Ans. Integrals have numerous real-life applications, such as calculating the area of irregular shapes in engineering and architecture, determining the total distance traveled by an object in physics, finding the average value of a quantity over a given interval, and solving differential equations in various scientific fields.
4. Are there different types of integrals?
Ans. Yes, there are different types of integrals, such as definite integrals, indefinite integrals, and improper integrals. Definite integrals are used to find the exact value of the accumulated quantity over a specific interval, while indefinite integrals give a family of functions that have the same derivative. Improper integrals are used when the interval of integration is infinite or when the function being integrated has singularities.
5. What is the relationship between derivatives and integrals?
Ans. Derivatives and integrals are closely related in calculus. The derivative of a function represents its rate of change, while the integral of a function represents its accumulated value. The fundamental theorem of calculus establishes the connection between derivatives and integrals, stating that taking the derivative of an integral gives the original function, and integrating the derivative gives the original function up to a constant.
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